U.S. patent application number 12/482636 was filed with the patent office on 2010-02-11 for method and system for predicting acoustic fields based on generalized moving frame acoustic holography.
This patent application is currently assigned to KOREA RESEARCH INSTITUTE OF STANDARDS AND SCIENCE. Invention is credited to Hyu-Sang Kwon.
Application Number | 20100036622 12/482636 |
Document ID | / |
Family ID | 41653717 |
Filed Date | 2010-02-11 |
United States Patent
Application |
20100036622 |
Kind Code |
A1 |
Kwon; Hyu-Sang |
February 11, 2010 |
METHOD AND SYSTEM FOR PREDICTING ACOUSTIC FIELDS BASED ON
GENERALIZED MOVING FRAME ACOUSTIC HOLOGRAPHY
Abstract
A method and system for predicting acoustic fields based on
generalized moving frame acoustic holography are disclosed. The
method includes acquiring a first wavenumber spectrum on a
measurement plane according to a moving coordinate system,
converting the first wavenumber spectrum to a second wavenumber
spectrum on a reference coordinate system using a relative velocity
between the measurement plane and a medium, converting the second
wavenumber spectrum to a third wavenumber spectrum on a prediction
plane using an acoustic wave propagation theory, converting the
third wavenumber spectrum to a fourth wavenumber spectrum on a
moving coordinate system using a relative velocity between the
medium and the prediction plane, and computing acoustic fields on
the prediction plane using the fourth wavenumber spectrum.
Inventors: |
Kwon; Hyu-Sang; (Daejeon,
KR) |
Correspondence
Address: |
HOLME ROBERTS & OWEN LLP
1700 LINCOLN STREET, SUITE 4100
DENVER
CO
80203
US
|
Assignee: |
KOREA RESEARCH INSTITUTE OF
STANDARDS AND SCIENCE
Daejeon
KR
|
Family ID: |
41653717 |
Appl. No.: |
12/482636 |
Filed: |
June 11, 2009 |
Current U.S.
Class: |
702/56 |
Current CPC
Class: |
G01H 3/125 20130101 |
Class at
Publication: |
702/56 |
International
Class: |
G06F 19/00 20060101
G06F019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Aug 7, 2008 |
KR |
10-2008-0077304 |
Claims
1. A method for predicting acoustic fields on a prediction plane by
measuring sound waves emitted from a sound source to a medium on a
measurement plane that makes a relative movement with respect to
the sound source, the method comprising: acquiring a first
wavenumber spectrum on the measurement plane according to a moving
coordinate system; converting the first wavenumber spectrum to a
second wavenumber spectrum on a reference coordinate system using a
relative velocity between the measurement plane and the medium;
converting the second wavenumber spectrum to a third wavenumber
spectrum on the prediction plane using an acoustic wave propagation
theory; converting the third wavenumber spectrum to a fourth
wavenumber spectrum on a moving coordinate system using a relative
velocity between the medium and the prediction plane; and computing
acoustic fields on the prediction plane using the fourth wavenumber
spectrum.
2. The method according to claim 1, wherein the first wavenumber
spectrum acquisition comprises performing a time-space Fourier
transform on sound pressures measured on the measurement plane.
3. The method according to claim 1, wherein the acoustic fields
computation comprises performing a time-space inverse Fourier
transform on the fourth wavenumber spectrum.
4. The method according to claim 1, wherein the prediction plane is
a sound source plane corresponding to the sound source.
5. The method according to claim 1, wherein if a velocity of the
medium is U.sub.m and a velocity of the measurement plane is
U.sub.h, with respect to a Cartesian coordinate system, two
different frequencies are f' and f, and the first wavenumber
spectrum is P.sub..xi.(k.sub..xi., k.sub..eta., .zeta..sub.h; f'),
the second wavenumber spectrum P.sub.x(k.sub.x, k.sub.y, z.sub.h;
f) is computed by P x ( k x , k y z h ; f ) = P .xi. ( k .xi. , k
.eta. , .zeta. h ; f ' + k .xi. 2 .pi. ( U h - U m ) ) .
##EQU00007##
6. The method according to claim 1, wherein if a velocity of the
medium is U.sub.m and a velocity of the prediction plane is
U.sub.s, with respect to a Cartesian coordinate system, two
different frequencies are f' and f, and the third wavenumber
spectrum is P.sub.x(k.sub.x, k.sub.y, z.sub.pred; f), the fourth
wavenumber spectrum P.sub..xi.(k.sub..xi., k.sub..eta., z.sub.pred;
f') is computed by P .xi. ( k .xi. , k .eta. , z pred ; f ' ) = P x
( k x , k y , z pred ; f - k .xi. 2 .pi. ( U s - U m ) ) .
##EQU00008##
7. A system for predicting acoustic fields on a prediction plane by
measuring sound waves emitted from a sound source to a medium on a
measurement plane that makes a relative movement with respect to
the sound source, the system comprising: a microphone array having
a plurality of microphones, for measuring sound waves on the
measurement plane; and an acoustic field prediction module for
predicting acoustic fields on the prediction plane using the
measurements received from the microphone array, wherein the
acoustic field prediction module acquires a first wavenumber
spectrum on the measurement plane according to a moving coordinate
system, converts the first wavenumber spectrum to a second
wavenumber spectrum on a reference coordinate system using a
relative velocity between the measurement plane and the medium,
converts the second wavenumber spectrum to a third wavenumber
spectrum on the prediction plane using an acoustic wave propagation
theory, converts the third wavenumber spectrum to a fourth
wavenumber spectrum on a moving coordinate system using a relative
velocity between the medium and the prediction plane, and computes
acoustic fields on the prediction plane using the fourth wavenumber
spectrum.
8. The system according to claim 7, wherein the microphone an-ay
includes a plurality of microphones arranged in a line or an arc at
predetermined intervals.
9. The system according to claim 7, wherein the acoustic field
prediction module acquires the first wavenumber spectrum by
performing a time-space Fourier transform on sound pressures
measured on the measurement plane.
10. The system according to claim 7, wherein the acoustic field
prediction module computes the acoustic fields on the prediction
plane by performing a time-space inverse Fourier transform on the
fourth wavenumber spectrum.
11. The system according to claim 7, wherein the prediction plane
is a sound source plane corresponding to the sound source.
12. The system according to claim 7, wherein if a velocity of the
medium is U.sub.m and a velocity of the measurement plane is
U.sub.h, with respect to a Cartesian coordinate system, two
different frequencies are f' and f, and the first wavenumber
spectrum is P.sub..xi.(k.sub..xi., k.sub..eta., .zeta..sub.h; f'),
the acoustic field prediction module computes the second wavenumber
spectrum P.sub.x(k.sub.x, k.sub.y, z.sub.h; f) by P x ( k x , k y ,
z h ; f ) = P .xi. ( k .xi. , k .eta. , .zeta. h ; f ' + k .xi. 2
.pi. ( U h - U m ) ) . ##EQU00009##
13. The system according to claim 7, wherein if a velocity of the
medium is U.sub.m and a velocity of the prediction plane is
U.sub.s, with respect to a Cartesian coordinate system, two
different frequencies are f' and f, and the third wavenumber
spectrum is P.sub.x(k.sub.x, k.sub.y, z.sub.pred; f), the acoustic
field prediction module computes the fourth wavenumber spectrum
P.sub..xi.(k.sub..xi., k.sub..eta., z.sub.pred; f') by P .xi. ( k
.xi. , k .eta. , z pred ; f ' ) = P x ( k x , k y , z pred ; f - k
.xi. 2 .pi. ( U s - U m ) ) . ##EQU00010##
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a method and system for
predicting acoustic fields, and more particularly to a method and
system for accurately predicting acoustic fields on a prediction
plane based on a source plane, a medium, and a measurement plane
that make a relative movement.
[0003] 2. Description of the Related Art
[0004] Many techniques for acquiring the hologram of acoustic
fields using sound pressure measurements and deriving information
about a sound source from the hologram have been proposed in both
private and military sectors. Farfield directivity information,
nearfield vector intensity information, surface velocity
information, total sound power information, etc. can be obtained
from the hologram of acoustic fields. A technology for detecting
the location and strength of a sound source by using the hologram
of acoustic fields may be used to find enemies in military
applications and to detect and eliminate a noise source or build a
noise wall in civilian industry sectors. Especially along with the
recent increased attention towards the environment and living
standards, there exists an increasing need for appropriately
dealing with noise sources based on accurate information about the
noise source.
[0005] Many acoustic holography techniques have been proposed Some
of the acoustic holography techniques are disclosed in J. D.
Maynard, E. G. Williams, and Y. Lee "NearField Acoustic Holography
(NAH): I. Theory of Generalized Holography and the Development of
NAH", Journal of the Acoustical Society of America, Vol. 74, No. 4,
pp. 1395-1413 (1985), W. A. Veronesi and J. D. Maynard "NearField
Acoustic Holography (NAH): II. Holographic Reconstruction
Algorithms and Computer Implementation", Journal of the Acoustical
Society of America, Vol. 81, No. 5, pp. 1307-1322(1988), U.S. Pat.
No. 4,415,996 entitled "Nonwavelength-Limited Holographic Acoustic
field Reconstruction" by J. D. Maynard and E. G. Williams, J. Hald
"Method of Spatial Transformation of Acoustic fields--A Unique
Technique for Scan-Based Near-Field Acoustic Holography Without
Restrictions on Coherence" Technical Review No. 1, 1989, BK
publication, and Loyau, J. C. Pascal, and P. Galliard, "Broadband
Acoustic Holography Reconstruction from Acoustic Intensity
Measurement" Journal of the Acoustical Society of America, Vol. 84,
No. 5, pp. 1744-1750 (1988).
[0006] Acoustic Holography (AH) is a technology for obtaining a
hologram on a reference plane called a hologram plane and
estimating the properties of sound waves at all spatial positions
of interest by analyzing the hologram.
[0007] FIG. 1 conceptually illustrates a conventional AH technique.
Referring to FIG. 1, the AH technique measures spatial acoustic
fields, namely a hologram, using a microphone array having a
plurality of microphones on an arbitary plane and estimates a
spatial distribution of acoustic fields from the hologram. This AH
technique is based on acoustic field mode interpretation that
relies on a spatial Fourier transform based on the
Kirchhoff-Hehmholts integral equation that is an acoustical
interpretation theory of phase-coherent acoustic fields.
[0008] Now a description will be made of a Moving Frame Acoustic
Holography (MFAH) technique proposed to improve the conventional AH
technique. Before the MFAH technique was proposed, conventional
measurement schemes required that the spatial position between the
microphone array and the sound source should be fixed. Therefore,
errors were inevitable when the sound source moved. Also, when air
being an acoustic medium flows, the conventional measurement
schemes have limitations in their application. Although studies
were continuously conducted on the issue, no specific solution was
found. In this context, the present inventors proposed an MFAH
technique based on a single linear array for the first time, and a
patent was granted for their MFAH technique (Korea Patent No.
217872). For details, see H.-S. Kwon and Y. -H. Kim, "Moving Frame
Technique for Planar Acoustic Holography", J. Acoust. Soc. Am.,
Vol. 103, No. 4, pp. 1734-1741(1998).
[0009] The MFAH technique estimates spatial information about a
sound source using temporal data from sound pressure measurements
according to the constant-velocity relative movement relationship
between the sound source and microphones. With the use of known
frequency and velocity information, a time-space variation is
detected based on the idea that the Doppler shift reveals the
time-space relationship. However, this MFAH technique derives a
modulated wavenumber spectrum from a frequency spectrum. If
modulated wavenumber spectra overlap because frequency components
are close to each other, if a source plane or a prediction plane
moves instead of a measurement plane, or if a medium moves, errors
occur.
[0010] While the above MFAH technique is important in that it is
the first to take into account the relative movement between a
sound source and a hologram plane with regards to the conventional
acoustic holography, it has many limitations in its effectiveness
in real-world implementation, such as a normal-state acoustic field
of a single frequency, the movement of measurement microphones,
etc.
[0011] Especially when modulated wavenumber spectra overlap because
frequency components are close to each other, when a source plane
or a prediction plane moves instead of a measurement plane, or when
a medium moves, severe problems are produced.
SUMMARY OF THE INVENTION
[0012] Therefore, the present invention has been made in view of
the above problems, and it is an object of the present invention to
provide a technique for accurately predicting acoustic fields on a
prediction plane, taking into account the relative movement of a
sound plane, a hologram plane, or a medium.
[0013] It is another object of the present invention to define
coordinate conversion relationships, generalize the coordinate
conversion relationships by formulation, and apply the generalized
coordinate conversion relationships to an acoustic field prediction
system.
[0014] To achieve the above and other objects, the present
invention provides a technique for expressing a sound source and a
medium, required for sound propagation and measurement points on
different coordinate systems and describing all of their relative
movements accordingly. Sound is propagated through the medium.
Hence, a relative movement of another coordinate system is
represented with respect to the coordinate system of the medium,
such that acoustic fields are represented on the same coordinate
system for which the relative movement is compensated for.
[0015] In accordance with the present invention, the above and
other objects can be accomplished by the provision of a method for
predicting acoustic fields on a prediction plane by measuring sound
waves emitted from a sound source to a medium on a measurement
plane that makes a relative movement with respect to the sound
source, the method including acquiring a first wavenumber spectrum
on the measurement plane according to a moving coordinate system,
converting the first wavenumber spectrum to a second wavenumber
spectrum on a reference coordinate system using a relative velocity
between the measurement plane and the medium, converting the second
wavenumber spectrum to a third wavenumber spectrum on the
prediction plane using an acoustic wave propagation theory,
converting the third wavenumber spectrum to a fourth wavenumber
spectrum on a moving coordinate system using a relative velocity
between the medium and the prediction plane, and computing acoustic
fields on the prediction plane using the fourth wavenumber
spectrum.
[0016] The first wavenumber spectrum acquisition may include
performing a time-space Fourier transform on sound pressures
measured on the measurement plane. The acoustic fields computation
may include performing a time-space inverse Fourier transform on
the fourth wavenumber spectrum.
[0017] In accordance with an aspect of the present invention, the
above and other objects can be accomplished by the provision of a
system for predicting acoustic fields on a prediction plane by
measuring sound waves emitted from a sound source to a medium on a
measurement plane that makes a relative movement with respect to
the sound source, the system including a microphone array having a
plurality of microphones, for measuring sound waves on the
measurement plane, and an acoustic field prediction module for
predicting acoustic fields on the prediction plane using the
measurements received from the microphone array. The acoustic field
prediction module acquires a first wavenumber spectrum on the
measurement plane according to a moving coordinate system, converts
the first wavenumber spectrum to a second wavenumber spectrum on a
reference coordinate system using a relative velocity between the
measurement plane and the medium, converts the second wavenumber
spectrum to a third wavenumber spectrum on the prediction plane
using an acoustic wave propagation theory, converts the third
wavenumber spectrum to a fourth wavenumber spectrum on a moving
coordinate system using a relative velocity between the medium and
the prediction plane, and computes acoustic fields on the
prediction plane using the fourth wavenumber spectrum.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The above and other objects, features and other advantages
of the present invention will be more clearly understood from the
following detailed description taken in conjunction with the
accompanying drawings, in which:
[0019] FIG. 1 conceptually illustrates a conventional AH
technique;
[0020] FIG. 2 illustrates a sound source coordinate system, a
medium coordinate system, and a hologram coordinate system with
respect to the Cartesian coordinate system;
[0021] FIG. 3 illustrates an acoustic field prediction system
according to an exemplary embodiment of the present invention;
[0022] FIG. 4 is a flowchart illustrating an operation performed by
the acoustic field prediction system illustrated in FIG. 3;
[0023] FIG. 5 is a block diagram illustrating an operation for
measuring sound pressures on a prediction plane using sound
pressures measured on a hologram plane (i.e. a measurement plane);
and
[0024] FIG. 6 illustrates a method for converting between a
reference coordinate system and a moving coordinate system.
DETAILED DESCRIPTION OF THE INVENTION
[0025] Exemplary embodiments of the present invention relate to a
technique for receiving sound waves propagated from a sound source
through a medium on a hologram plane (i.e. a measurement plane) and
predicting acoustic fields on a prediction plane using the sound
waves.
[0026] Specific features of the present invention will be made
apparent by exemplary embodiments of the present invention
described later. A description will be made of the exemplary
embodiments of the present invention with reference to the attached
drawings.
[0027] FIG. 2 illustrates a sound source coordinate system, a
medium coordinate system, and a hologram coordinate system with
respect to a Cartesian coordinate system. In the conventional AH
technique, sound waves are interpreted as independent sound waves
between parallel planes. For the convenience of description,
coordinate systems are shown with respect to the Cartesian
coordinate system in FIG. 2. However, it is clear to those skilled
in the art that the exemplary embodiment of the present invention
is applicable to various orthogonal coordinate systems such as a
cylindrical coordinate system, a spherical coordinate system, and
the like.
[0028] With regards to movement of a sound source or measurement
points, movements of two planes and a movement of a medium between
the two planes may be represented. It may be assumed that all
movements are made linearly at a constant velocity and directed
along an x axis, in view of the nature of coordinate systems.
Hereafter, for each coordinate system, a reference coordinate
system is represented as (x, y, z) and a moving coordinate system
that is synchronized to a movement of the sound source or the
measurement points is represented as (.xi.,.eta.,.zeta.). To
indicate the sound source coordinate system, the medium coordinate
system, and the hologram coordinate system, subscripts s, m, h are
used, respectively.
[0029] Referring to FIG. 2, regarding the relative movement of each
coordinate system, a sound source plane and a hologram plane are
parallel to each other in a surface-to-surface conversion
relationship. The medium is the space between the two planes,
through which sound waves are actually propagated. Therefore, the
behavior of sound waves may be interpreted with respect to the
medium. In this context, a coordinate system synchronized to the
movement of the medium is set as a reference, thus called a
reference coordinate system and sound waves are interpreted on the
reference coordinate system.
[0030] When the medium does not move, i.e. there is no flow in the
medium, the reference coordinate system is fixed. In this case, a
fixed-moving coordinate system conversion is performed for the
movement of the sound source or the hologram in each coordinate
system.
[0031] The same applies to the case where the medium moves at a
constant speed. In this case, the behavior of all sound waves are
interpreted and represented on the reference coordinate system that
moves together with the medium. Acoustic fields of another moving
coordinate system may be represented on a coordinate system
relative to the reference coordinate system.
[0032] For the source plane, a moving coordinate system fixed to
the sound source may be represented as a relative coordinate system
that makes a U.sub.s-U.sub.m relative movement (U.sub.s is the
velocity of the source and U.sub.m is the velocity of the medium,
with respect to an absolute coordinate system). Similarly for the
hologram plane (the velocity of the hologram is expressed as
U.sub.h with respect to the absolute coordinate system), a moving
coordinate system fixed to the positions of the measurement points
may be represented as a relative coordinate system by which to
represent a relative movement with respect to the medium.
[0033] With the introduction of the relative coordinate systems,
the behavior of all sound waves maybe expressed as acoustic fields
on a reference coordinate system synchronized to the movement of
the medium and acoustic fields in a real coordinate system (a
coordinate system observed by an observer) and the relationship
between these coordinate systems may be clarified.
[0034] A description will be made of an example of predicting
acoustic fields on the measurement plane using the sound pressures
measured on the hologram plane based on the reference coordinate
system, the relative coordinate systems of the moving coordinate
systems, and the coordinate conversion relationships.
[0035] FIG. 3 illustrates an acoustic field prediction system
according to an exemplary embodiment of the present invention.
Referring to FIG. 3, a sound source 300 emits sound waves having
various wavelengths. As these sound waves propagate through a
medium, they maybe analyzed as acoustic fields 301. A microphone
array 310 is a measurement device having a plurality of
microphones, which may measure sound pressure on a hologram plane
(i.e. a measurement plane) determined by the position of the
microphone array 310. The microphone array 310 may be formed into
various configurations, for example, a two-dimensional array, a
linear one-dimensional array, or an arc-shaped one-dimensional
array.
[0036] In FIG. 3, an acoustic field prediction module 320 receives
sound pressure measurements from the microphone array 310 and
performs an operation for predicting acoustic fields on an
arbitrary prediction plane using the sound pressure measurements.
The prediction plane may be determined in various ways, but is
generally or primarily determined to be a sound source plane on
which the sound source 300 is placed. That is, the acoustic field
prediction module 320 may predict acoustic fields on the source
plane. Hereinafter, a description will be made of a case where the
source plane is determined as the prediction plane, by way of
example.
[0037] FIG. 4 is a flowchart illustrating an operation performed by
the acoustic field prediction system illustrated in FIG. 3.
[0038] Referring to FIG. 4, sound pressures on the hologram plane
are measured through the microphone array 310 in step S410. In step
S420, a wavenumber spectrum may be obtained on the measurement
plane by a time-space Fourier transform of the sound pressure
measurements. For the convenience of description, the wavenumber
spectrum on the hologram plane (i.e. the measurement plane) is
referred to as a first wavenumber spectrum.
[0039] In accordance with the exemplary embodiment of the present
invention, since the source plane, the medium, or the measurement
plane makes a relative movement, sound waves may be analyzed by
converting the various coordinate systems illustrated in FIG. 2.
Specifically, all coordinate systems are based on the movement of
the medium. A coordinate system that moves in synchronization to
the movement of the medium is called "a reference coordinate
system".
[0040] For this purpose, conversion to an (x, y, z) coordinate
system synchronized to the velocity U.sub.m of the medium is
performed. That is, the first wavenumber spectrum is converted to a
wavenumber spectrum on the reference coordinate system in step
S430. For the convenience of description, the result from
converting the first wavenumber spectrum to the wavenumber spectrum
on the reference coordinate system is referred to as a second
wavenumber spectrum.
[0041] Because the first and second wavenumber spectrums are
wavenumber spectrums on the hologram plane (i.e. the measurement
plane), they need to be represented on the source plane (i.e. the
prediction plane). For this purpose, the second wavenumber spectrum
is converted to a wavenumber spectrum on the prediction plane by a
conventional acoustic wave propagation theory in step S440. This
wavenumber spectrum on the prediction plane is referred to as a
third wavenumber spectrum, for the convenience of description. The
third wavenumber spectrum is one represented on the reference
coordinate system.
[0042] If the source plane (i.e. the prediction plane) moves
according to U.sub.s, the third wavenumber spectrum on the
reference coordinate system may be represented on a coordinate
system synchronized to the sound source. To do so, the third
wavenumber spectrum is converted to a wavenumber spectrum on a
moving coordinate system in step S450. For the convenience of
description, the result from converting the third wavenumber
spectrum to the wavenumber spectrum on the moving coordinate system
is referred to as a fourth wavenumber spectrum.
[0043] In step S460, sound pressures on the prediction plane may be
measured by an inverse Fourier transform of the fourth wavenumber
spectrum.
[0044] FIG. 5 is a block diagram illustrating an operation for
measuring sound pressures on the prediction plane using sound
pressures measured on the hologram plane (i.e. the measurement
plane). Since FIG. 5 describes an exemplary case where a relative
movement is made along the x axis, sound pressures and wavenumber
spectrums are expressed only with respect to .xi. and x axes. Yet,
it is clear to those skilled in the art that the illustrated case
of FIG. 5 is applicable to relative movements along various axes.
Each step of FIG. 5 has its counterpart in FIG. 4. That is, the
result of step S501 in FIG. 5 may be obtained by performing step
S401 in FIG. 4.
[0045] Referring to FIG. 5, sound pressures p.sub..xi.(.xi..sub.h,
.eta..sub.hk, .zeta..sub.h; t) on the hologram plane (the
measurement plane) are measured through the microphone array 310 in
step S501.
[0046] In step S502, the first wavenumber spectrum
P.sub..xi.(k.sub..xi., k.sub..eta., .zeta..sub.h; f') is obtained
by a time-space Fourier transform of the measurements of the sound
pressures p.sub..xi.(.xi..sub.h, .eta..sub.h, .zeta..sub.h; t).
[0047] The first wavenumber spectrum P.sub..xi.(k.sub..xi.,
k.sub..eta., .lamda..sub.h; f') is on a moving coordinate system
and thus it is converted to a wavenumber spectrum on the reference
coordinate system. That is, the second wavenumber spectrum
P.sub.x(k.sub.x, k.sub.y, z.sub.h; f) is computed in step S503.
Generally, z.sub.h=.zeta..sub.h.
[0048] Then the third wavenumber spectrum P.sub.x(k.sub.x, k.sub.y,
z.sub.pred; f) is computed by an acoustic wave propagation theory
in step S504. For details of the computation of a wavenumber
spectrum by the acoustic wave propagation theory, refer to i) J. D.
Maynard, E. G. Williams, and Y. Lee "Nearfield Acoustic Holography
(NAH): I. Theory of Generalized Holography and the Development of
NAH", Journal of the Acoustical Society of America, Vol. 74, No. 4,
pp. 1395-1413(1985), ii) W. A. Veronesi and J. D. Maynard,
"Nearfield Acoustic Holography (NAH): II Holographic Reconstruction
Algorithms and Computer Implementation", Journal of the Acoustical
Society of America, Vol. 81, No. 5, pp. 1307-1322 (1988), iii) J.
Hald, "Method of Spatial Transformation of Acoustic fields--A
Unique Technique for Scan-Based Near-Field Acoustic Holography
Without Restrictions on Coherence", Technical Review No. 1, 1989,
BK publication, and iv) H.-S. Kwon and Y. -H. Kim, "Moving Frame
Technique for Planar Acoustic Holography", J. Acoust. Soc. Am.,
Vol. 103, No. 4, pp. 1734-1741 (1998), which are well known to
those skilled in the art and thus will not be described herein.
[0049] The third wavenumber spectrum P.sub.x(k.sub.s, k.sub.y,
z.sub.pred; f) is a wavenumber spectrum on the reference coordinate
system and thus is converted to a wavenumber spectrum on a moving
coordinate system. That is, the fourth wavenumber spectrum
P.sub..xi.(k.sub..xi., k.sub..eta., z.sub.pred; f') is computed in
step S505.
[0050] In step S506, sound pressures p.sub..xi.(.xi..sub.pred,
.eta..sub.pred, .zeta..sub.pred; t) on the source plane (i.e. the
prediction plane) are measured by a time-space inverse Fourier
transform of the fourth wavenumber spectrum P.sub..xi.(k.sub..xi.,
k.sub..eta., z.sub.pred; f'). Generally,
z.sub.pred=.zeta..sub.pred.
[0051] In the illustrated case of FIG. 5, the time-space Fourier
transform and wavenumber spectrum conversion based on the acoustic
wave propagation theory may be carried out conventionally. However,
step 503, that is, the step of converting a wavenumber spectrum on
a moving coordinate system to a wavenumber spectrum on the
reference coordinate system, and step 505, that is, the step of
converting a wavenumber spectrum on the reference coordinate system
to a wavenumber spectrum on a moving coordinate system are
performed as follows.
[0052] FIG. 6 illustrates a method for converting between
coordinate systems that make a relative movement. While FIG. 6
describes the case of an x-axis relative movement by way of
example, the illustrated case of FIG. 6 may apply to relative
movements along various axes.
[0053] Referring to FIG. 6, the wavenumber spectrum relationship
between coordinate systems that make relative movements lies in a
recombination of frequency components and wavenumber components.
When the medium and the hologram plane move together, the relative
movement U of the hologram plane is expressed as
U.sub.h-U.sub.m.
[0054] The conversion from the first wavenumber spectrum to the
second wavenumber spectrum amounts to re-arrangement of spectrum
components.
[0055] That is, a component 601 of the first wavenumber spectrum
P.sub..xi.(k.sub..xi., k.sub..eta., .zeta..sub.h; f') moves in the
second wavenumber spectrum P.sub.x(k.sub.x, k.sub.y, z.sub.h; f)
according to k.sub..xi.=k.sub.x, k.sub..eta.=k.sub.y, and
f = f ' + k x 2 .pi. U = f ' + k x 2 .pi. ( U h - U m )
##EQU00001##
[0056] That is, the component 601 on the moving coordinate system
also exists on the reference coordinate system, but at a different
frequency from in the moving coordinate system. In other words,
although the component 601 on the moving coordinate system has an
equal wavenumber to that of a component 602 on the reference
coordinate system, the frequency band of the wavenumber changes to
.omega.=(2.pi.f), not .omega.'=(2.pi.f'). In this case, the
relationship between .omega.' and .omega. depends on the relative
movement of the hologram plane, U=(U.sub.h-U.sub.m).
[0057] The relationship between the first wavenumber spectrum
P.sub..xi.(k.sub..xi., k.sub..eta., .lamda..sub.h; f') and the
second wavenumber spectrum P.sub.x(k.sub.x, k.sub.y, z.sub.h; f) is
expressed as
P x ( k x , k y z h ; f ) = P .xi. ( k .xi. , k .eta. , .zeta. h ;
f ' + k .xi. 2 .pi. ( U h - U m ) ) [ Equation 1 ] ##EQU00002##
[0058] Now a description will be made of the relationship between
the third wavenumber spectrum P.sub.x(k.sub.x, k.sub.y, z.sub.pred;
f) and the fourth wavenumber spectrum P.sub..xi.(k.sub..xi.,
k.sub..eta., z.sub.pred; f'). The third wavenumber spectrum
P.sub.x(k.sub.x, k.sub.y, z.sub.pred; f) is on the reference
coordinate system and thus is converted to the fourth wavenumber
spectrum P.sub..xi.(k.sub..xi., k.sub..eta., z.sub.pred; f') by
reversely performing the foregoing operation.
[0059] That is, the conversion between the third and fourth
wavenumber spectrums is equivalent to re-arrangement of spectrum
components.
[0060] A component of the third wavenumber spectrum
P.sub.x(k.sub.x, k.sub.y, z.sub.pred; f) moves in the fourth
wavenumber spectrum P.sub..xi.(k.sub..xi., k.sub..eta., z.sub.pred;
f') according to k.sub..xi.=k.sub.x, k.sub..eta.=k.sub.y, and
f ' = f - k .xi. 2 .pi. U = f - k .xi. 2 .pi. ( U h - U m ) .
##EQU00003##
[0061] That is, although the component 602 on the reference
coordinate system has an equal wavenumber to that of the component
601 on the moving coordinate system, the frequency band of the
wavenumber changes to .omega., not .omega.'.
[0062] The relationship between the third wavenumber spectrum
P.sub.x(k.sub.x, k.sub.y, z.sub.pred; f) and the fourth wavenumber
spectrum P.sub..xi.(k.sub..xi., k.sub..eta., z.sub.pred; f') is
expressed as
P .xi. ( k .xi. , k .eta. , z pred ; f ' ) = P x ( k x , k y , z
pred ; f - k .xi. 2 .pi. ( U s - U m ) ) [ Equation 2 ]
##EQU00004##
[0063] The above-described technique is related to accurate
prediction of acoustic fields according to a relative movement of
the source plane, the medium, or the hologram plane. The relative
movement may be quantitated in various conventional ways, which
will not be described in detail herein.
[0064] The exemplary embodiment of the present invention
illustrated in FIG. 5 has been described above in the context of a
plurality of equations representing the respective steps, that is,
the step of converting sound pressures to a wavenumber spectrum,
the step of converting the wavenumber spectrum to a wavenumber
spectrum on a reference coordinate system, the step of converting
the wavenumber spectrum on the reference coordinate system to a
wavenumber spectrum on the prediction plane by an acoustic wave
propagation theory, the step of converting the wavenumber spectrum
on the prediction plane to a wavenumber spectrum on a moving
coordinate system, and the step of converting the converted
wavenumber spectrum to sound pressures. However, it is clearly
understood to those skilled in the at that a plurality of equations
corresponding to respective steps may be replaced with one or more
integrated equation Therefore, it may be said that a technique for
predicting acoustic fields using the integrated equation (including
a matrix) is a simple modification of the present invention.
[0065] A major example of substituting a single equation for a
plurality of equations, Statistically Optimized Nearfield Acoustic
Holography (SONAH) will be described. Equations 3 and 4 describe an
exemplary Fourier transform and inverse Fourier transform with
respect to the Cartesian coordinate system.
P ( k x , k y , z ; f ) = F { p ( x , y , z ; t ) } = .intg. -
.infin. .infin. .intg. - .infin. .infin. .intg. - .infin. .infin. p
( x , y , z ; t ) j2 .pi. ft - j ( k x x + k y y ) t x y [ Equation
3 ] p ( x , y , z ; t ) = F - 1 { P ( k x , k y , z ; f ) } = 1 ( 2
.pi. ) 2 .intg. - .infin. .infin. .intg. - .infin. .infin. .intg. -
.infin. .infin. P ( k x , k y , z ; f ) - j2.pi. ft - j ( k x x + k
y y ) f k x k y [ Equation 4 ] ##EQU00005##
[0066] A Fourier transform and inverse Fourier transform may be
expressed as matrices in a discrete domain. In this case, the
matrix corresponding to a Fourier transform may be represented as F
and the matrix corresponding to an inverse Fourier transform may be
represented as F.sup.-1. Meanwhile, a matrix corresponding to a
reference to moving coordinate system conversion and conversion
based on an acoustic wave propagation theory may be represented as
T. In this case, sound pressure on the measurement plane and sound
pressure on the prediction plane is placed in the following
relationship.
p(x.sub.pred, y.sub.pred, z.sub.pred; f)=F.sup.+TF p(x.sub.h,
y.sub.h, z.sub.h; f) [Equation 5]
[0067] In this case, three matrices may be converted to a single
matrix T'.
p ( x pred , y pred , z pred ; f ) = F + TFp ( x h , y h , z h ; f
) = T ' p ( x h , y h , z h ; f ) [ Equation 6 ] ##EQU00006##
[0068] The single matrix T' described in Equation 6 is no more than
a conversion of the plurality of equations proposed in accordance
with the exemplary embodiment of the present invention. It may be
said that the technique for predicting acoustic fields on a
prediction plane using Equation 6 falls within the scope of the
present invention.
[0069] The specific equations described above in the exemplary
embodiment of the present invention are used for illustrative
purposes only, to which the present invention is not limited.
[0070] As is apparent from the above description, the exemplary
embodiments of the present invention provide a technique for
analyzing acoustic fields on the same coordinate system for which a
relative movement is compensated for by representing a relative
movement of another coordinate system with respect to the
coordinate system of a medium.
[0071] Therefore, acoustic fields can be accurately predicted on a
prediction plane, even when a sound plane, a hologram plane, or a
medium makes a relative movement on various coordinate systems (the
Cartesian coordinate system, a cylindrical coordinate system, a
spherical coordinate system, etc.).
[0072] Although the preferred embodiments of the present invention
have been disclosed for illustrative purposes, those skilled in the
art will appreciate that various modifications, additions and
substitutions are possible, without departing from the scope and
spirit of the invention as disclosed in the accompanying
claims.
* * * * *